almost $\mathbb{R}$-paracompact

Definition

A space X is almost -paracompact iff every open covering of X of cardinality has an open locally finite refinement whose union is dense in X. It is equivalent to almost $\Aleph$-paracompactness.

Reference

• Cao Ji-Ling, Weakly closed multifunctions and paracompactness, Internat. J. Math and Math. Sci. Vol.16, No.2, pp.345-350 (1993).